A recently observed spectrum of Pc states exhibits a strong link to Σc¯D(*) thresholds. In spite of successful molecular interpretations, we still push forward to wonder whether there exist finer ...structures. Utilizing the effecitve Lagrangians respecting heavy quark symmetry and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we investigate the Σc¯D(*) interactions and three Pc states. We confirm that Pc (4312) and Pc (4440) are good candidates of Σc¯D and Σc¯D∗ molecules with spin-1/2, respectively. Unlike other molecular calculations, our results indicate the Pc (4457) signal might be a mixture of spin-3/2 and spin-1/2 Σc¯D∗ molecules, where the latter one appears to be an excitation of Pc (4440) . Therefore we conclude that, confronting three LHCb Pc signals, there may exist not three, but four molecular states.
We present a detailed discussion on the doubly charmed baryon
Ξ
cc
production at the RHIC and LHC via the proton–nucleus (
p
–N) and nucleus–nucleus (N–N) collision modes. The extrinsic charm ...mechanism via the subprocesses
g
+
c
→
(
c
c
)
n
+
c
¯
and
c
+
c
→
(
c
c
)
n
+
g
together with the gluon-gluon fusion mechanism via the subprocess
g
+
g
→
(
c
c
)
n
+
c
¯
+
c
¯
have been taken into consideration, where the intermediate diquark is in
n
=
1
S
0
6
-state or
3
S
1
3
¯
-state, respectively. Total and differential cross sections have been discussed under various collision energies. To compare with the
Ξ
cc
production via proton-proton collision mode at the LHC, we observe that sizable
Ξ
cc
events can also be generated via
p
–N and N–N collision modes at the RHIC and LHC. For examples, about
8.1
×
10
7
and
6.7
×
10
7
Ξ
cc
events can be accumulated in
p
-Pb and Pb-Pb collision modes at the LHC within one operation year.
A
bstract
The spectrum and relativistic wave functions of
B
c
system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each
J
P
state. ...Our study shows that there are three categories of
J
P
states. The first category contains 0
−
and 0
+
states, which are
1
S
0
dominant state with a small amount of
P
wave and
3
P
0
dominant state with a small amount of
S
wave, respectively. The second category includes the natural parity states, such as 1
−
, 2
+
, 3
−
, etc. Taking the 1
−
state as an example, we study it in two cases. One is the
3
S
1
dominant state with a small amount of
P
and
D
waves, and the other is the
3
D
1
dominant state but contains a large amount of
S
and
P
wave components. The third category includes the unnatural parity states, such as 1
+
, 2
−
, 3
+
, etc. For the 1
+
spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two
1
P
1
−
3
P
1
mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.
Mass spectra and wave functions of the
J
P
=
1
2
+
(
bcq
) baryons are calculated by the relativistic Bethe–Salpeter equation (BSE) with considering the mixing effects between the
1
+
and
0
+
(
bc
...)-diquarks inside. Based on the diquark picture, the three-body problem of baryons is transformed into two two-body problems. The BSE and wave functions of the
0
+
diquark are given, and then solved numerically to obtain the effective mass spectra and form factors. Also we present the wave functions at zero point for the (
bc
)-diquark. Considering the obtained diquark form factors, the (
bcq
) baryons are then described by the BSE as the bound state of a diquark and a light quark, where the interaction kernel includes the inner transitions between the
0
+
and
1
+
diquarks. The general wave function of the
1
2
+
(
bcq
) baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between
Ξ
bc
(
Ω
bc
)
and
Ξ
bc
′
(
Ω
bc
′
)
in ground states are computed and determined to be small (
∼
1
%
). The numerical results indicate that it is a good choice to take
Ξ
bc
and
Ξ
bc
′
as the baryon states with the inside (
bc
)-diquarks occupying the definite spin.
Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Miller's transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, ...one-loop triangle, two-loop vacuum, and two-loop sunset diagrams, respectively. The codimension of derived GKZ-hypergeometric system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. Taking GKZ-hypergeometric systems of one-loop self energy, massless one-loop triangle, and two-loop vacuum diagrams as examples, we present in detail how to perform triangulation and how to construct canonical series solutions in the corresponding convergent regions. The series solutions constructed for these hypergeometric systems recover the well known results in literature.
Based on the nonrelativistic quantum chromodynamics factorization formalism, the polarization parameters λθϕ and λϕ of prompt J/ψ hadroproduction for CMS and LHCb are analyzed in the helicity frame ...and calculated at QCD next-to-leading order for the first time. For prompt J/ψ production, we take into account the feed-down contributions from χcJ and ψ(2S) decays. The theoretical predictions for the polarization parameters λθϕ and λϕ of J/ψ are presented. Using the theoretical results, we perform a simultaneous fit to the experimental measurements of the yield and polarization of J/ψ hadroproduction, and find that the results describe the experimental measurements at the LHC quite well.
In this paper we derive the next-to-leading-order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium J/Ψ or ϒ. The ultraviolet divergences in the real ...corrections are removed through operator renormalization, which is performed in the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g., μF = 3mc for c → J/Ψ and μF = 3mb for b → ϒ, which can be evolved to any scale via the use of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial application of these fragmentation functions, we study J/Ψ (ϒ) production at a high-luminosity e+e− collider running at an energy around the Z pole, which could be a suitable platform for testing the fragmentation function.
A
bstract
In the paper, we calculate the fragmentation functions for
g
→
B
c
and
g
→
B
c
∗
. The ultraviolet divergences in the calculation are removed through the renormalization of the operator ...definition of the fragmentation functions under the modified minimal subtrac- tion scheme. We then obtain the fragmentation functions
D
g
→
B
c
(
z, μ
F
) and
D
g
→
B
c
∗
(
z, μ
F
), which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for
b
¯
→
B
c
(
B
c
∗
) and
c
→
B
c
(
B
c
∗
).
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